Process and apparatus for automatically determining the modulation transfer function of focal plane array cameras

ABSTRACT

In a process for automatically determining the modulation transfer function (MTF) of a focal plane array (FPA) cameras, a test grid is used to generate a beat whose amplitude corresponds to that of the grid image to be measured, without the sampling MTF. (The image of the test grid has a spatial frequency in the detector plane that is detuned with respect to the Nyquist frequency of the detector array. The test grid covers a range of at least half a beat period, and then, regardless of the actual phase position, the modulation amplitude is determined therefrom. Comparative MTF measurements are thereby permitted without the influence of the sampling effect of an FPA, and particularly the MTF measurement in real time suitable for the application to moving images.

BACKGROUND AND SUMMARY OF THE INVENTION

[0001] This application claims the priority of German patent document101 53 237.7, filed Oct. 31, 2001, the disclosure of which is expresslyincorporated by reference herein.

[0002] The invention relates to a process for automatically determiningthe modulation transfer function (MTF) of a focal plane array (FPA)camera and a system for its implementation.

[0003] Various measuring methods are known for determining the MTF, forexample, from Vollmershausen and Driggers, “Analysis of Sampled ImagingSystems”, Bellingham, Wash., 2000. Traditional techniques require staticimaging of a test structure onto the detector plane.

[0004] One object of the invention is to provide a system that canmeasure the modulation transfer function MTF of a focal plane array(FPA) camera in real time. Such a system is particularly advantageous inthe case of a moving camera or moving scenery, or when measuring theresidual stabilization error while exciting vibrations.

[0005] This and other objects and advantages are achieved by the methodand apparatus according to the invention, for automatically determiningthe MTF of an FPA camera, in which a test grid is used to generate abeat whose amplitude corresponds to that of the grid image to bemeasured, without the sampling MTF. The image of the test grid has aspatial frequency in the detector plane that is detuned with respect tothe Nyquist frequency of the detector array. The test grid covers arange of at least half a beat period, and then, regardless of the actualphase position, the modulation amplitude is determined therefrom.Comparative MTF measurements are thereby permitted without beingaffected by the sampling effect of an FPA, and particularly the MTFmeasurement in real time, which is suitable for application to movingimages.

[0006] Other objects, advantages and novel features of the presentinvention will become apparent from the following detailed descriptionof the invention when considered in conjunction with the accompanyingdrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0007]FIG. 1 is a schematic diagram of apparatus according to theinvention for measuring MTF of a focal plane array camera;

[0008]FIG. 2 shows the image of a test grid pattern projected onto adetector array of the focal plane array camera of FIG. 1;

[0009]FIG. 3.a is a general view of a sinusoidal beat signal;

[0010]FIG. 3.b is a view of beat fractions in the proximity of half theNyquist frequency;

[0011]FIG. 4.a is a view of the alignment of the used beat grid;

[0012]FIG. 4.b is a view of the beat grid with range markers;

[0013]FIG. 4.c the graphic representation of the sine or cosine fit;

[0014]FIGS. 5.a to 5 .d are views of measuring results with various fitparameters; and

[0015]FIG. 6 is a flow diagram that illustrates the processing accordingto the invention.

DETAILED DESCRIPTION OF THE DRAWINGS

[0016] Theoretical Observation

[0017]FIG. 1 is a schematic diagram of apparatus for measuring the MTFof an FPA camera using the method according to the invention. For thispurpose a test grid 1 is positioned in front of a black body 2 so as tomask the illumination from an energy source such as a heating plate (notshown).

[0018] Openings 1 a in the test grid 1 form a pattern of illuminationwhich is focused via a collimator lens 3, onto a detector array in thedetector plane of an FPA camera 4 whose MTF is to be determined. Imagedata output from the FPA camera is provided to an image processing unit5, for evaluation in the manner described hereinafter. In addition, adisplay 6 or other graphic user interface is provided to present outputinformation from the image-processor, in a human readable or detectableformat.

[0019]FIG. 2 shows the image 1 .b of the test grid projected onto anarray of detector elements 7 disposed in the detector plane of the FPAcamera. An intensity distribution is thus created there whose periodicwaveform f(x), shown graphically below the detector array, will bedescribed here by a sinusoidal function: $\begin{matrix}{{f(x)} = {\sin \left( {\frac{2\pi}{p}*x} \right)}} & {{Eq}.\quad (1.1)}\end{matrix}$

[0020] where the x coordinate is oriented perpendicular to the gridgaps, and P indicates the length of the period. The intensitydistribution is sampled by individual detector elements at discretepoints 8, so that $\begin{matrix}{{f\left( x_{n} \right)} = {\sin \left( {\frac{2\pi}{p}*x_{n}} \right)}} & {{Eq}.\quad (1.2)}\end{matrix}$

[0021] indicates the value of the function which is measured by the nthdetector element at the position x_(n).

[0022] If the spatial frequency of the imaged grid structure correspondsprecisely to the Nyquist frequency of the detector, two detectorelements exist per period. In the latter case . . . $\begin{matrix}{x_{n} = {n*\frac{P}{2}\quad \left( {{for}\quad {Nyquist}\quad {{grid}!}} \right)}} & {{Eq}.\quad (1.3)}\end{matrix}$

[0023] However, since the frequency of the imaged grid is to be slightlydetuned with respect to the Nyquist frequency of the detector, a summandΔ is added which indicates the amount of the detuning: $\begin{matrix}{x_{n} = {n*\left( {\frac{P}{2} + \Delta} \right)}} & {{Eq}.\quad (1.4)}\end{matrix}$

[0024] By inserting Equation (1.4) in Equation (1.2), the following isobtained $\begin{matrix}{{f\left( x_{n} \right)} = {{\sin \left( {{n\quad \pi} + {n*\frac{2\pi*\Delta}{p}}} \right)}\quad = {{{\sin \left( {n\quad \pi} \right)}*{\cos \left( {\frac{2\pi*\Delta}{p}*n} \right)}} + \quad {{\cos \left( {n\quad \pi} \right)}*{\sin \left( {\frac{2\pi*\Delta}{p}*n} \right)}}}}} & {{Eq}.\quad (1.5)}\end{matrix}$

[0025] Since n corresponds to the number of detector elements andtherefore assumes only integral values, the factor sin (n n) is alwaysequal to 0, while the factor cos(n n) is alternately equal to +1 and −1.Therefore, Equation (1.5) can be simplified to $\begin{matrix}{{f\left( x_{n} \right)} = {{\left( {- 1} \right)^{n}{\sin \left( {\frac{2\pi}{p^{*}}*n} \right)}\quad {with}\text{:}\quad P^{*}} = \frac{P}{\Delta}}} & {{Eq}.\quad (1.6)}\end{matrix}$

[0026] This result can be interpreted such that the detector elements 7measure a periodic waveform of an intensity with the period P* thatdepends on the amount of the “detuning”. This response can be treated asa “beat”, and the beat frequency is$v = {\frac{1}{\left( {2\pi \quad P^{*}} \right)}.}$

[0027] As an example, FIG. 3.a shows a measurement with a grid “detuned”with respect to the Nyquist frequency; the period of the beat amounts toapproximately 12 pixels. This example also shows that, in accordancewith Equation 1.6, the measured values of the intensities arealternately at a positive and a negative sinusoidal function.

[0028] It is important that the amplitude of the beat correspondsprecisely to the amplitude which is measured in the optimal phaseposition of the imaged grid. Thus, because the beat function Equation(1.6) is reconstructed from the measured values by means of a fit, andthe amplitude is introduced as an adaptable parameter, the desiredamplitude of the intensity modulation is obtained even without actuallysetting the optimal phase position.

[0029] In the case of a beat frequency that is generated close to onehalf of the Nyquist frequency, the analysis is slightly more complicatedbecause, instead of two samples, now four samples per period arepresent; that is, four detector elements apply to each line pair of thegrid. The two oscillatory fractions in the case of the Nyquist frequencybecome four fractions which, in addition to the sinusoidal oscillations,also contain the positive and negative cosinusoidal oscillations.

[0030] If the discrete scanning points $\begin{matrix}{x_{n} = {n*\left( {\frac{P}{4} + \Delta} \right)}} & {{Eq}.\quad (1.7)}\end{matrix}$

[0031] are placed in Equation (1.2), the following is obtained:$\begin{matrix}{{f\left( x_{n} \right)} = {\sin \left( {{n*\frac{\pi}{2}} + {n*\frac{2\pi*\Delta}{P}}} \right)}} & {{Eq}.\quad (1.8)} \\{= {{{\sin \left( {n*\quad \frac{\pi}{2}} \right)}{\cos \left( {\frac{2\pi*\Delta}{p}*n} \right)}} + {{\cos \left( {n\quad*\frac{\pi}{2}} \right)}{\sin \left( {\frac{2\pi*\Delta}{p}*n} \right)}}}} & {{Eq}.\quad (1.9)}\end{matrix}$

[0032] The cases are therefore differentiated as follows:

[0033] Case 1: The Sinusoidal Fractions $\begin{matrix}{{n = 0},2,4,{\ldots \quad = {{2{v:\quad {f\left( x_{2v} \right)}}} = {\left( {- 1} \right)^{v}{\sin \left( {\frac{2\pi}{P^{*}}*2v} \right)}}}}} & {{Eq}.\quad (1.10)}\end{matrix}$

[0034] with:${P^{*} = {\frac{P}{\Delta} = {{periodicity}\quad {in}\quad n}}},$

[0035] periodicity in n, that is, number of pixels or: $\begin{matrix}{f_{({0,\quad 4,\quad \ldots})} = {\sin \left( {\frac{2\pi}{p^{*}}*n} \right)}} & {{Eq}.\quad (1.11)}\end{matrix}$

$\begin{matrix}{f_{({2,\quad 6,\quad \ldots})} = {- {\sin \left( {\frac{2\pi}{p^{*}}*n} \right)}}} & {{Eq}.\quad (1.12)}\end{matrix}$

[0036] Case 2: Cosinusoidal Fractions: $\begin{matrix}{{n = 1},3,5,{\ldots \quad = {{{2v} + 1}:{f\left( {x_{{{2v} + 1})} = {\left( {- 1} \right)^{v}{\cos \left( {\frac{2\pi}{P^{*}}*\left( {{2v} + 1} \right)} \right)}}} \right.}}}} & {{Eq}.\quad (1.13)} \\{{{{or}\text{:}\quad f_{({1,5,\quad \ldots}\quad)}} = {\cos \left( {\frac{2\pi}{p^{*}}*n} \right)}}\quad} & {{Eq}.\quad (1.14)} \\{{f_{({3,7,\quad \ldots})} = {- {\cos \left( {\frac{2\pi}{p^{*}}*n} \right)}}}\quad} & {{Eq}.\quad (1.15)}\end{matrix}$

[0037]FIG. 3.b shows four beat fractions for a computed example with abeat period of 32 pixels.

[0038] Each even pixel represents alternately the positive or thenegative sinusoidal oscillation, and each odd pixel representsalternately the positive or the negative cosinusoidal oscillation. As aresult, the number of pixels or of gray values per oscillatory fractionamounts only to a quarter of the total number.

[0039] The Analyzing Software

[0040] The software must be capable of reading out the area of thedetector chip on which a representative intensity waveform of the beatgrid is imaged, and of computing the MTF from the resulting gray valuewaveform.

[0041] If the image of the test grid shifts in the detector plane (forexample, as a result of the vibrations affecting the camera), it shouldbe known for each individual image where the grid is located at thetime. Since the MTF of the camera is to be checked in the horizontal aswell as in the vertical axis, the grid structure may be alignedhorizontally or vertically. (See FIG. 4.a.) This should also beautomatically detected by the program.

[0042] Tracing and Read-Out of the Grid Line

[0043] Two markers 1 .c are placed next to the grid, in the form of twoholes which indicate the length of the grid structure and have a defineddistance from the grid center. (See FIGS. 2 and 4.b.) The holes of themarkers appear in the image as bright spots because the heating plate isvisible through the holes.

[0044] The software is depicted in the form of a flow diagram in FIG. 6.After an image is acquired (Step 601), a search is made (Step 602) ineach individual image for the brightest gray value in a defined range ofpixels around the position of the markers from the preceding individualimage. The search area should be sufficient to cover from image to imagethe jumps that occur in practice, for example, while vibrations of thecamera are excited.

[0045] When the actual position of the markers has been found, the lineor column (line n in FIG. 1) is thereby determined on which the gridcenter is imaged, and is read out.

[0046] Determination of the MTF by Means of Beat Grids

[0047] The gray-value waveform of the image of a grid is read out withina line or column in Step 603, and further processing depends on whetherthe grid frequency is close to the Nyquist frequency, or rather is closeto half the Nyquist frequency, as determined in Step 604. In the case ofthe former, one of two methods may be selected, (Step 606) for furtherprocessing (Steps 607 and 608), while in the case of the latter, threealternatives (Steps 607 a, 608 a and 610) may be selected (Step 610), asdiscussed below. In either case, the measured values are first sorted inStep 605 or Step 609 as applicable. (See equations 1.6, 1.10 and 1.13)

[0048] A) MIN-MAX Method

[0049] In the min-max method, the minimum and maximum gray values aredetermined. The difference between the minimum and maximum valuescorresponds to the transmitted contrast (Step 612). The latter is theused (Step 13) to calculate the MTF according to $\begin{matrix}{{MTF} = {\frac{\pi}{4} \cdot {C_{grid}/C_{ref}}}} & {{Eq}.\quad (1.16)}\end{matrix}$

[0050] Cref being a reference contrast for spatial frequency 0.

[0051] This method however results in a systematic error when the grayvalues are situated such that they do not record the maximum or minimumof the beat amplitude. The presence of noise additionally falsifies thedetermined amplitude value.

[0052] B) Sine Fit

[0053] In this method the mean value is determined from the measuredgray values, and is subtracted from all measured values. If a beatfrequency is analyzed which is generated close to one half of theNyquist frequency, the measured values thus converted are then furthersorted (Step 609) corresponding to Equation (1.10) and Equation (1.13),so that in each case half of all measured values are available for thesine fit and the cosine fit. In this case, it should also be taken intoaccount that, in each group, the preceding sign of each second measuredvalue must be inverted. The actual sine or cosine fit is performed in amanner which is well known to those skilled in the art, using standardnumerical techniques.

[0054] This process is more precise than the Min-Max method. Moreover,in addition to the amplitude, information is obtained concerning thephase.

[0055] C) Direct Amplitude Determination

[0056] Since, in the case of measurements close to half the Nyquistfrequency, the gray values are distributed to a sinusoidal and acosinusoidal function of the same amplitude, this amplitude can bedetermined directly (Step 611), without a fit, by using therelationship.

sin² φ+cos² φ=1

[0057] If, analogous to Point B) above, the mean value is subtractedfrom the measured gray values, the sum of squares of the gray values oftwo adjacent pixels respectively results in the square of the modulationamplitude. However, an error occurs because the measured values whichare to be assigned to the sinusoidal and cosinusoidal functions aretaken at slightly different arguments. The larger the number of themeasured values per half period of the sinusoidal or cosinusoidalfunction the smaller the error is. When the amplitude values thusobtained are averaged over half a period length or an integral multiplethereof, the error will precisely disappear.

[0058] Illustrating the Measuring Method by Means of an Image Sequence

[0059] To illustrate the method, the MTF measurement on a vibratingcamera is shown in the image sequence of FIGS. 5.a to 5 .d. Theindividual images were generated per “screen shot”. For this purpose,both the amplitude values and the associated fit curves according to theabove-described method B are shown.

[0060] This image sequence shows the possibilities of the suggested MTFmeasuring method: Although the position and the resolution of the imagedtest grid changes from one individual image to the next, the transmittedcontrast (and thus the MTF) can be determined for each individual imagefrom the fit parameter “amplitude”. As a result, the MTF can bedetermined, as described previously. In the illustrated image,differences in the amplitudes occur to a factor 4. The correlation withthe image resolution of the screen shots is evident. The reason for suchdrastic differences is a noise-type vibration excitation of the cameraand as a result an accidental distribution of the camera deflectionsduring an individual image exposure.

[0061] The foregoing disclosure has been set forth merely to illustratethe invention and is not intended to be limiting. Since modifications ofthe disclosed embodiments incorporating the spirit and substance of theinvention may occur to persons skilled in the art, the invention shouldbe construed to include everything within the scope of the appendedclaims and equivalents thereof.

1. A process for the automatically determining a modulation transferfunction of focal plane array cameras, said method comprising: providinga test grid, having an image with a spatial frequency in the detectorplane that is detuned with respect to the Nyquist frequency or arational fraction of the Nyquist frequency, of a detector array of saidcamera; using said test grid to generate a beat whose amplitudecorrespond to amplitude of the grid image to be measured, without thesampling the modulation transfer function; wherein the test grid coversa range of at least half a beat period; regardless of actual phaseposition, the modulation amplitude is determined therefore.
 2. A processaccording to claim 1, wherein: within a line or column, the gray-valuewaveform of the image of the grid is read out; and thereafter, minimumand maximum gray values are determined, the difference between theminimal and maximal value corresponding to transmitted contrast.
 3. Theprocess according to claim 1, wherein; from measured gray values, a meanvalue is determined and is subtracted from all measured values to formconverted values; thereafter, the converted values are sortedcorresponding to${n = 0},2,4,{\ldots = {{2{v:\quad {f\left( x_{2v} \right)}}} = {\left( {- 1} \right)^{v}{\sin \left( {\frac{2\pi}{P^{*}}*2v} \right)}}}}$and${n = 1},3,5,{{\ldots = {{2v} + 1}};{f\left( {x_{{{2v} + 1})} = {\left( {- 1} \right)^{v}{\cos \left( {\frac{2\pi}{P^{*}}*\left( {{2v} + 1} \right)} \right)}}} \right.}}$

whereby in each case half of all measured values are available for asine fit and a cosine fit, in each group a preceding sign of everysecond measured value being inverted.
 4. The process according to claim1, wherein: amplitude of the beats is determined directly, without afit, by subtracting a mean value from the measured gray values; the sumof squared of the gray values of adjacent pixels respectively results ina square of the modulation amplitude; and the thus obtained amplitudevalues are averaged over half a period length or an integral multiplethereof.
 5. Apparatus for implementing the process according to claim 1,comprising: an energy source; a test grid having a grid structure formasking energy from said source to form a pattern; means for focusingsaid pattern on a detector array in a focal plane camera; and an imageprocessor couple to receive an output signal from said camera; whereinthe test grid has spacer markers whose spacing corresponds to length ofthe grid structure.